Evaluate The Function F ( X ) = X 2 + 7 X + 2 F(x)=x^2+7x+2 F ( X ) = X 2 + 7 X + 2 At The Given Values Of The Independent Variable And Simplify.a. F ( 6 F(6 F ( 6 ]b. F ( X + 2 F(x+2 F ( X + 2 ]c. F ( − X F(-x F ( − X ]a. F ( 6 ) = □ F(6) = \square F ( 6 ) = □ (Simplify Your Answer.)

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Introduction

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In this article, we will evaluate the function $f(x)=x^2+7x+2$ at the given values of the independent variable and simplify the results. We will also explore the function's behavior when the input is modified by adding or subtracting a constant.

Evaluating $f(6)$

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To evaluate $f(6)$, we need to substitute $x=6$ into the function $f(x)=x^2+7x+2$. This means we will replace every instance of $x$ with $6$ and then simplify the resulting expression.

$f(6) = (6)^2 + 7(6) + 2$

Using the order of operations, we first calculate the exponentiation:

$f(6) = 36 + 7(6) + 2$

Next, we multiply $7$ by $6$:

$f(6) = 36 + 42 + 2$

Finally, we add the numbers together:

$f(6) = 80$

Therefore, $f(6) = 80$.

Evaluating $f(x+2)$

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To evaluate $f(x+2)$, we need to substitute $x+2$ into the function $f(x)=x^2+7x+2$. This means we will replace every instance of $x$ with $x+2$ and then simplify the resulting expression.

$f(x+2) = (x+2)^2 + 7(x+2) + 2$

Using the order of operations, we first calculate the exponentiation:

$f(x+2) = (x^2 + 4x + 4) + 7(x+2) + 2$

Next, we distribute the $7$ to the terms inside the parentheses:

$f(x+2) = x^2 + 4x + 4 + 7x + 14 + 2$

Finally, we combine like terms:

$f(x+2) = x^2 + 11x + 20$

Therefore, $f(x+2) = x^2 + 11x + 20$.

Evaluating $f(-x)$

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To evaluate $f(-x)$, we need to substitute $-x$ into the function $f(x)=x^2+7x+2$. This means we will replace every instance of $x$ with $-x$ and then simplify the resulting expression.

$f(-x) = (-x)^2 + 7(-x) + 2$

Using the order of operations, we first calculate the exponentiation:

$f(-x) = x^2 - 7x + 2$

Therefore, $f(-x) = x^2 - 7x + 2$.

Conclusion

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In this article, we evaluated the function $f(x)=x^2+7x+2$ at the given values of the independent variable and simplified the results. We also explored the function's behavior when the input is modified by adding or subtracting a constant. The results show that the function can be evaluated at specific values of $x$ and that the function's behavior changes when the input is modified.

Final Thoughts

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Evaluating functions at specific values of the independent variable is an important concept in mathematics. It allows us to understand the behavior of the function and make predictions about its output. In this article, we saw how to evaluate the function $f(x)=x^2+7x+2$ at specific values of $x$ and how to simplify the results. We also explored the function's behavior when the input is modified by adding or subtracting a constant. This knowledge can be applied to a wide range of mathematical problems and is an essential tool for anyone working with functions.

References

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• [1] "Functions" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra-functions
• [2] "Evaluating Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/funcevaluate.html

Note: The references provided are for general information and are not specific to the function $f(x)=x^2+7x+2$. They are intended to provide additional resources for readers who want to learn more about functions and evaluating functions.

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Introduction

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In our previous article, we evaluated the function $f(x)=x^2+7x+2$ at the given values of the independent variable and simplified the results. We also explored the function's behavior when the input is modified by adding or subtracting a constant. In this article, we will answer some frequently asked questions about evaluating functions and provide additional insights into the behavior of the function $f(x)=x^2+7x+2$.

Q&A

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Q: What is the difference between evaluating a function at a specific value and evaluating a function at a variable?

A: Evaluating a function at a specific value means substituting a numerical value into the function and simplifying the resulting expression. Evaluating a function at a variable means substituting a variable or expression into the function and simplifying the resulting expression.

Q: How do I evaluate a function at a negative value?

A: To evaluate a function at a negative value, simply substitute the negative value into the function and simplify the resulting expression. For example, to evaluate $f(-x)$, we would substitute $-x$ into the function $f(x)=x^2+7x+2$ and simplify the resulting expression.

Q: Can I evaluate a function at a fraction or decimal value?

A: Yes, you can evaluate a function at a fraction or decimal value. Simply substitute the fraction or decimal value into the function and simplify the resulting expression.

Q: How do I evaluate a function at a variable that is raised to a power?

A: To evaluate a function at a variable that is raised to a power, simply substitute the variable and power into the function and simplify the resulting expression. For example, to evaluate $f(x^2)$, we would substitute $x^2$ into the function $f(x)=x^2+7x+2$ and simplify the resulting expression.

Q: Can I evaluate a function at a variable that is multiplied by a constant?

A: Yes, you can evaluate a function at a variable that is multiplied by a constant. Simply substitute the variable and constant into the function and simplify the resulting expression.

Q: How do I evaluate a function at a variable that is added to a constant?

A: To evaluate a function at a variable that is added to a constant, simply substitute the variable and constant into the function and simplify the resulting expression.

Q: Can I evaluate a function at a variable that is subtracted from a constant?

A: Yes, you can evaluate a function at a variable that is subtracted from a constant. Simply substitute the variable and constant into the function and simplify the resulting expression.

Additional Insights

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Evaluating Functions with Multiple Variables

When evaluating a function with multiple variables, we need to substitute each variable into the function and simplify the resulting expression. For example, to evaluate $f(x,y)=x^2+7x+2y$, we would substitute $x$ and $y$ into the function and simplify the resulting expression.

Evaluating Functions with Absolute Values

When evaluating a function with absolute values, we need to consider the sign of the expression inside the absolute value. For example, to evaluate $f(x)=|x^2+7x+2|$, we would consider the sign of the expression $x^2+7x+2$ and simplify the resulting expression accordingly.

Evaluating Functions with Square Roots

When evaluating a function with square roots, we need to consider the sign of the expression inside the square root. For example, to evaluate $f(x)=\sqrt{x^2+7x+2}$, we would consider the sign of the expression $x^2+7x+2$ and simplify the resulting expression accordingly.

Conclusion

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In this article, we answered some frequently asked questions about evaluating functions and provided additional insights into the behavior of the function $f(x)=x^2+7x+2$. We also explored the concept of evaluating functions at specific values and variables, and how to simplify the resulting expressions. By understanding how to evaluate functions, we can gain a deeper understanding of the behavior of functions and make predictions about their output.

Final Thoughts

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Evaluating functions is an essential concept in mathematics, and it has many practical applications in fields such as physics, engineering, and economics. By mastering the art of evaluating functions, we can solve complex problems and make informed decisions. In this article, we provided a comprehensive guide to evaluating functions, including frequently asked questions and additional insights into the behavior of the function $f(x)=x^2+7x+2$. We hope that this article has been helpful in your understanding of evaluating functions and that you will continue to explore this fascinating topic.

References

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• [1] "Functions" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra-functions
• [2] "Evaluating Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/funcevaluate.html